We examine several high performance code families, including (extended) binary Golay code [1]}, Reed-Muller code family [2]}, and BCH code family (Goppa code family) [3]}, and summarize their coded bit-string length \(n\) , data bit-string length \(k\) , and minimum Hamming distance \(d_{min}\)  in a lookup table in the supplementary material. One example is shown in Fig. REF  (b). The \((22,10,8)\)  code appends 12bits after the 10bit uncoded data string (Fig. REF  (a)), and the codebook has minimum distance \(d_{min} = 8\) .
